Simplify 2/(3x^2+12x)+8/(2x)

$\frac{2}{3 x^{2} + 12 x} + \frac{8}{2 x}$

Step 1

Simplify each term.

Factor $3 x$ out of $3 x^{2} + 12 x$ .

Factor $3 x$ out of $3 x^{2}$ .

$\frac{2}{3 x (x) + 12 x} + \frac{8}{2 x}$

Factor $3 x$ out of $12 x$ .

$\frac{2}{3 x (x) + 3 x (4)} + \frac{8}{2 x}$

Factor $3 x$ out of $3 x (x) + 3 x (4)$ .

$\frac{2}{3 x (x + 4)} + \frac{8}{2 x}$

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8$ .

$\frac{2}{3 x (x + 4)} + \frac{2 \cdot 4}{2 x}$

Cancel the common factors.

Factor $2$ out of $2 x$ .

$\frac{2}{3 x (x + 4)} + \frac{2 \cdot 4}{2 (x)}$

Cancel the common factor.

$\frac{2}{3 x (x + 4)} + \frac{2 \cdot 4}{2 x}$

Rewrite the expression.

$\frac{2}{3 x (x + 4)} + \frac{4}{x}$

Step 2

To write $\frac{4}{x}$ as a fraction with a common denominator, multiply by $\frac{3 (x + 4)}{3 (x + 4)}$ .

$\frac{2}{3 x (x + 4)} + \frac{4}{x} \cdot \frac{3 (x + 4)}{3 (x + 4)}$

Step 3

Write each expression with a common denominator of $3 x (x + 4)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{x}$ by $\frac{3 (x + 4)}{3 (x + 4)}$ .

$\frac{2}{3 x (x + 4)} + \frac{4 (3 (x + 4))}{x (3 (x + 4))}$

Reorder the factors of $x (3 (x + 4))$ .

$\frac{2}{3 x (x + 4)} + \frac{4 (3 (x + 4))}{3 x (x + 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 + 4 (3 (x + 4))}{3 x (x + 4)}$

Step 5

Simplify the numerator.

Factor $2$ out of $2 + 4 \cdot 3 (x + 4)$ .

Factor $2$ out of $2$ .

$\frac{2 (1) + 4 \cdot 3 (x + 4)}{3 x (x + 4)}$

Factor $2$ out of $4 \cdot 3 (x + 4)$ .

$\frac{2 (1) + 2 (2 \cdot 3 (x + 4))}{3 x (x + 4)}$

Factor $2$ out of $2 (1) + 2 (2 \cdot 3 (x + 4))$ .

$\frac{2 (1 + 2 \cdot 3 (x + 4))}{3 x (x + 4)}$

Multiply $2$ by $3$ .

$\frac{2 (1 + 6 (x + 4))}{3 x (x + 4)}$

Apply the distributive property.

$\frac{2 (1 + 6 x + 6 \cdot 4)}{3 x (x + 4)}$

Multiply $6$ by $4$ .

$\frac{2 (1 + 6 x + 24)}{3 x (x + 4)}$

Add $1$ and $24$ .

$\frac{2 (6 x + 25)}{3 x (x + 4)}$

Simplify 2/(3x^2+12x)+8/(2x)

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